I assume you want a scripting solution. One way to do it is extract the numbers numbercolbox in the display tree that holds the parameter estimates. In the Fit Model report it is the first numeric column in the "Parameter Estimates" outline box. Below is an jsl example. I don't have access to JMP7, but it works in JMP9.

I don't know if I really understand your problem, but after a linear fit (also any other) in a scatter plot you get a table with parameter estimtes. I can right-click on the table an chose "make into table" which makes a new JMP table.